Laboratoire de l'Informatique et du Parallélisme » CVP

#! /opt/sage/sage

# @file cvp-run-01.sage

# Compute a polynomial from the CVP of the function vector.

# Return the polynomial, the error and the (one of) point(s) where this error

# is reached.

#

scriptName = os.path.basename(__file__)

var('x')

contFracMaxErr = 10^-7

#

def initialize_env():

    """

    Load all necessary modules.

    """

    compiledSpyxDir = \

        "/home/storres/recherche/arithmetique/pobysoPythonSage/compiledSpyx"

    if compiledSpyxDir not in sys.path:

        sys.path.append(compiledSpyxDir)

    """

    As of Sage versions above or equal to 7.0, appending MPFI is not needed and

    crashes the program.

    if not 'mpfi' in sage.misc.cython.standard_libs:

        sage.misc.cython.standard_libs.append('mpfi')

    """

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sollya_lib.sage")

#    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageMpfr.spyx")

#    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageGMP.spyx")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/pobyso.py")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageSLZ.sage")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageNumericalOperations.sage")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageRationalOperations.sage")

    # Matrix operations are loaded by polynomial operations.

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sagePolynomialOperations.sage")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageRunSLZ.sage")

    load("/home/storres/recherche/arithmetique/cvp/src/functions_for_cvp.sage")

# End initialize_env.

#

initialize_env()

from sageMpfr import *

from sageGMP  import *

import sys

#

def usage(scriptName):

    write = sys.stderr.write

    write("Usage:\n")

    write("  " + scriptName + " <func> <lowerBound> <upperBound> <coeffsExpList> \n")

    write(" " * (len(scriptName) + 3))

    write("<coeffsPrecList> <minCoeffsBoundExpList>\n")

    write(" " * (len(scriptName) + 3))

    write("<maxCoeffsBoundExpList> <pointList> <precision>\n")

    write("\nArguments:\n")

    write("  func\n")

    write("  lowerBound\n")

    write("  upperBound\n")

    write("  coeffsExpList\n")

    write("  coeffsExpList\n")

    write("  minCoeffsBoundExpList\n")

    write("  maxCoeffsBoundExpList\n")

    write("  maxCoeffsBoundExpList\n")

    write("  maxCoeffsBoundExpList\n\n")

    ##

    sys.exit(1)

# End usage

#

argsCount = len(sys.argv)

#

## Arguments recovery

if argsCount < 10:

    usage(scriptName)

funcAsString                    = sys.argv[1]

lowerBoundAsString              = sys.argv[2]

upperBoundAsString              = sys.argv[3]

coeffsExpListAsString           = sys.argv[4]

coeffsPrecListAsString          = sys.argv[5] 

minCoeffsBoundExpListAsString   = sys.argv[6] 

maxCoeffsBoundExpListAsString   = sys.argv[7]

pointsListAsString              = sys.argv[8]

precisionAsString               = sys.argv[9]

#

## Arguments conversion

### Create first the rational field that will be used throughout the script.

precision               = int(precisionAsString)

realField               = RealField(precision)

#

func(x)                 = sage_eval(funcAsString, cmds="var('x')")

try:

    lowerBound          = realField(lowerBoundAsString)

except:

    lowerBoundAsRat     = QQ(lowerBoundAsString)

    lowerBound          = realField(lowerBoundAsRat)

try:

    upperBound          = realField(upperBoundAsString)

except:

    upperBoundAsRat     = QQ(upperBoundAsString)

    upperBound          = realField(upperBoundAsRat)

coeffsExpList           = sage_eval(coeffsExpListAsString)

coeffsPrecList          = sage_eval(coeffsPrecListAsString)

minCoeffsBoundExpList   = sage_eval(minCoeffsBoundExpListAsString)

maxCoeffsBoundExpList   = sage_eval(maxCoeffsBoundExpListAsString)

pointsList              = sage_eval(pointsListAsString)

#

## Debug printing.

sys.stderr.write("func: " + func._assume_str().replace("_SAGE_VAR_","",100) + \

                 "\n")

sys.stderr.write("precision: " + str(precision) + "\n")

sys.stderr.write("lowerBound: " + str(lowerBound) + "\n")

sys.stderr.write("upperBound: " + str(upperBound) + "\n")

sys.stderr.write("coeffsExpList: " + str(coeffsExpList) + "\n")

sys.stderr.write("coeffsPrecList: " + str(coeffsPrecList) + "\n")

sys.stderr.write("minCoeffsBoundExpList: " + str(minCoeffsBoundExpList) + "\n")

sys.stderr.write("maxCoeffsBoundExpList: " + str(maxCoeffsBoundExpList) + "\n")

sys.stderr.write("pointsList: " + str(pointsList) + "\n")

#

poly = cvp_cvp_polynomial(func, 

                          lowerBound, 

                          upperBound,

                          coeffsExpList,

                          coeffsPrecList, 

                          minCoeffsBoundExpList, 

                          maxCoeffsBoundExpList,

                          pointsList,

                          realField)

sys.stderr.write(str(poly) + "\n")

(maxisList,maxErr)  = cvp_polynomial_error_func_maxis(func,

                                                      poly, 

                                                      lowerBound, 

                                                      upperBound,

                                                      realField,

                                                      contFracMaxErr)

(maxErrPoint, maxErrPointErr) = cvp_func_abs_max_for_points(func,

                                                            maxisList)

sys.stdout.write(str(maxErrPoint) + " " + str(maxErr.n(prec=53)) + "\n")

sys.exit(int(0))